Lesson 11.3: Two-Part Analysis: Quantitative

Introduction

Data Insights questions on the GMAT can often feel overwhelming due to their complexity and the need for careful integration of multiple pieces of information. This lesson is specifically focused on the Two-Part Analysis: Quantitative questions. These questions typically feature a two-column answer grid, necessitating the selection of linked answers. By the end of the lesson, students will be able to:

• Understand the structure of the two-part answer grid and how to interpret it.
• Set up and recognize linked quantitative relationships between the two parts of each question.
• Efficiently test candidate answer pairs to identify the correct answer.
• Solve a range of quantitative two-part analysis questions successfully.
• Manage two linked answers without confusion across the columns.

Two-Column Answer Grid

Structure of the Two-Part Answer Grid

In the Two-Part Analysis format, answers are displayed in a grid format, often seen as follows:

Column 1 (Answer A)	Column 2 (Answer B)
Option 1	Option A
Option 2	Option B
Option 3	Option C
Option 4	Option D

Each answer selection from Column 1 will correspond to a selection in Column 2. For example, if you select Option 2 from Column 1, you will need to evaluate it against all options in Column 2.

This formatting requires an understanding of how the two answers relate. They are usually dependent; this means that the choice in Column A influences the possible choices in Column B.

Example of Understanding the Answer Grid

Question: An item was sold for a price $ x $. If its cost was $ y $, what is the profit percentage?

Assume the options provided in the matrix are:

Column 1 (Value of $ x $)	Column 2 (Value of $ y $)
$100$	$80$
$150$	$100$
$200$	$120$
$250$	$150$

To calculate profit percentage, we use the formula:

$$\text{Profit Percentage} = \frac{x - y}{y} \times 100$$

1. For $ x = 100 $ and $ y = 80 $:

$$\text{Profit Percentage} = \frac{100 - 80}{80} \times 100 = 25\%$$

1. For $ x = 150 $ and $ y = 100 $:

$$\text{Profit Percentage} = \frac{150 - 100}{100} \times 100 = 50\%$$

1. For $ x = 200 $ and $ y = 120 $:

$$\text{Profit Percentage} = \frac{200 - 120}{120} \times 100 = 66.67\%$$

1. For $ x = 250 $ and $ y = 150 $:

$$\text{Profit Percentage} = \frac{250 - 150}{150} \times 100 = 66.67\%$$

Here we can see that selecting the correct value from Column 1 and interpreting its relationship with the respective value from Column 2 is crucial for finding your answer.

Setting Up Linked Quantitative Relationships

In a Two-Part Analysis question, setting up the linked relationship properly can make the solving process systematic. Let's consider how to approach establishing these relationships through a structured methodology.

Common Methodology

1. Identify the Variables: Identify what each column represents and what variable each answer option links to. Ensure you understand the context for those variables.
2. Establish the Relationships: Write down the mathematical expressions that show how the two parts (Column 1 and Column 2) are related to each other.
3. Use Substitution: Substitute values of one answer option into the expression tied to the other.
4. Check Validity: Verify whether pairs of answers lead to logical and consistent outputs.
5. Cross-Verify: Check each candidate combination iteratively to manage confusion.

Worked Example

Question: A store sells $ p $ items at a price $ q $ each. If the total revenue is $ 1200 $, what can be represented in a two-part table?

Assuming the options are:

• Column 1: $ p $: 10, 20, 30, 40
• Column 2: $ q $: 120, 60, 40, 30

Here we need $ p \times q = 1200 $. Let’s check:

1. For $ p = 10 $, $ q = 120 $:

$$10 \times 120 = 1200 \quad \text{(Valid)}$$

1. For $ p = 20 $, $ q = 60 $:

$$20 \times 60 = 1200 \quad \text{(Valid)}$$

1. For $ p = 30 $, $ q = 40 $:

$$30 \times 40 = 1200 \quad \text{(Valid)}$$

1. For $ p = 40 $, $ q = 30 $:

$$40 \times 30 = 1200 \quad \text{(Valid)}$$

Here, all pairs satisfy the total revenue condition. This means we have validated all combinations successfully. Evaluating the relationships and confirming the logical output is crucial for time management and accuracy.

Testing Candidate Pairs Efficiently

Once you understand the connections between columns, you want to develop quick strategies to test pairs in order to arrive at the correct answer effectively.

Efficient Testing Techniques

1. Choose the Most Obvious Pair First: Start with easy pairs (those that seem to yield clear results) rather than complex combinations.
2. Elimination Strategy: If one part is clear and leads you to a logical contradiction in the other, immediately eliminate that pair.
3. Calculate: Use basic arithmetic or algebraic manipulation to quickly verify the truth of a chosen pair.
4. Manage Columns Not to Mix: When solving, keep track of which answer you pick from which column to ensure no mix-up occurs—taking notes can help here.

Example Problem

Question: If a tap can fill a tank in $ x $ hours and another can empty it in $ y $ hours, what is the time taken to fill the tank when both are open simultaneously?

Assuming:

• Column 1 $ x $: 5, 10, 15, 20
• Column 2 $ y $: 10, 20, 30, 40

To set this up, we know:

$$\text{Time Taken} = \frac{xy}{x-y}$$

Check pairs:

1. For $ x = 5 $, $ y = 10 $:

$$\text{Time Taken} = \frac{5 \times 10}{5 - 10} = -10 \quad \text{(Invalid)}$$

1. For $ x = 10 $, $ y = 20 $:

$$\text{Time Taken} = \frac{10 \times 20}{10 - 20} = -20 \quad \text{(Invalid)}$$

1. For $ x = 15 $, $ y = 30 $:

$$\text{Time Taken} = \frac{15 \times 30}{15 - 30} = -30 \quad \text{(Invalid)}$$

1. For $ x = 20 $, $ y = 10 $:

$$\text{Time Taken} = \frac{20 \times 10}{20 - 10} = 20 \quad \text{(Valid)}$$

Here, $ x = 20 $ and $ y = 10 $ shows a valid way to fill the tank.

Conclusion

In this lesson, students has developed essential skills for navigating the complexities of Two-Part Analysis: Quantitative questions. We have explored the structure of the answer grid, how to analyze linked relationships, effective testing strategies, and practical examples to reinforce understanding. Being proficient with these concepts can significantly impact performance on GMAT Data Insights questions.

Study Notes

• The Two-Part Analysis requires linking answers across two columns.
• Understand the question context to establish quantifiable relationships.
• Use simple arithmetic checks to validate candidate pairs efficiently.
• Keep track of chosen answers to avoid confusion between columns.
• Time management is crucial: start with easier pairs and eliminate invalid options quickly.